Demographics Stats

age_years n
2 6
3 23
4 34
5 15
gender n
F 47
M 31
knower_level_cp_subset age_years n
CP 3 4
CP 4 23
CP 5 13
subset 2 6
subset 3 19
subset 4 11
subset 5 2

Results

Correct set chosen

Combining both overt set selection and correct counting (participants are correct if they’ve selected the correct set, or counted correctly.)

By trial

Doesn’t seem to be any differences between small and large sets, only between CP and subset knowers.

## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`

By participant

Each dot is a participant. Accurracy in set chosen against age (years, continuous) looks linear.

## `summarise()` has grouped output by 'id', 'magnitude'. You can override using
## the `.groups` argument.

## `summarise()` has grouped output by 'id', 'magnitude',
## 'knower_level_cp_subset'. You can override using the `.groups` argument.
## `geom_smooth()` using formula = 'y ~ x'

## `summarise()` has grouped output by 'id', 'magnitude'. You can override using
## the `.groups` argument.

Regressions

Base model

correct_set_chosen_or_correct_count ~ magnitude + age_zscored + (1|id) + (1|trial_ratio) Effect of age

## boundary (singular) fit: see help('isSingular')
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct_set_chosen_or_correct_count ~ magnitude + age_zscored +  
##     (1 | id) + (1 | trial_ratio)
##    Data: df.trial
## 
##      AIC      BIC   logLik deviance df.resid 
##    404.5    425.2   -197.2    394.5      463 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0733 -0.2833  0.1717  0.4165  2.1881 
## 
## Random effects:
##  Groups      Name        Variance  Std.Dev. 
##  id          (Intercept) 3.612e+00 1.901e+00
##  trial_ratio (Intercept) 5.404e-10 2.325e-05
## Number of obs: 468, groups:  id, 78; trial_ratio, 6
## 
## Fixed effects:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)      1.6905     0.3424   4.937 7.92e-07 ***
## magnitudesmall   0.1224     0.2858   0.428    0.668    
## age_zscored      1.7078     0.3244   5.264 1.41e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) mgntds
## magnitdsmll -0.398       
## age_zscored  0.268  0.020
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##               Chisq Df Pr(>Chisq)    
## (Intercept) 24.3778  1  7.918e-07 ***
## magnitude    0.1834  1     0.6685    
## age_zscored 27.7116  1  1.408e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Not registered: CP knowledge + magnitude, no age

correct_set_chosen_or_correct_count ~ knower_level_cp_subset + magnitude + (1|id) + (1|trial_ratio) Effect of knower level, no effect of magnitude. ***??? Model failed to converge

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct_set_chosen_or_correct_count ~ knower_level_cp_subset +  
##     magnitude + (1 | id) + (1 | trial_ratio)
##    Data: df.trial
## 
##      AIC      BIC   logLik deviance df.resid 
##    413.7    434.5   -201.9    403.7      463 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.8528 -0.3171  0.1457  0.3726  1.9106 
## 
## Random effects:
##  Groups      Name        Variance  Std.Dev.
##  id          (Intercept) 4.434e+00 2.105730
##  trial_ratio (Intercept) 8.513e-06 0.002918
## Number of obs: 468, groups:  id, 78; trial_ratio, 6
## 
## Fixed effects:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                    3.3310     0.5663   5.882 4.05e-09 ***
## knower_level_cp_subsetsubset  -3.0553     0.6736  -4.536 5.74e-06 ***
## magnitudesmall                 0.1222     0.2855   0.428    0.669    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) knw___
## knwr_lvl_c_ -0.784       
## magnitdsmll -0.229 -0.018
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00711028 (tol = 0.002, component 1)
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                          Chisq Df Pr(>Chisq)    
## (Intercept)            34.6016  1  4.046e-09 ***
## knower_level_cp_subset 20.5735  1  5.739e-06 ***
## magnitude               0.1831  1     0.6688    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Registered: CP knowledge + magnitude + age

correct_set_chosen_or_correct_count ~ knower_level_cp_subset + magnitude + age_zscored + (1|id) + (1|trial_ratio) Effect of age, no effect of KL or magnitude.

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct_set_chosen_or_correct_count ~ knower_level_cp_subset +  
##     magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
##    Data: df.trial
## 
##      AIC      BIC   logLik deviance df.resid 
##    403.0    427.9   -195.5    391.0      462 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2273 -0.2908  0.1592  0.3879  2.1262 
## 
## Random effects:
##  Groups      Name        Variance  Std.Dev. 
##  id          (Intercept) 3.443e+00 1.8554417
##  trial_ratio (Intercept) 1.930e-07 0.0004394
## Number of obs: 468, groups:  id, 78; trial_ratio, 6
## 
## Fixed effects:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                    2.3604     0.5257   4.490 7.11e-06 ***
## knower_level_cp_subsetsubset  -1.3026     0.7080  -1.840  0.06578 .  
## magnitudesmall                 0.1227     0.2862   0.429  0.66808    
## age_zscored                    1.2808     0.3701   3.460  0.00054 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) knw___ mgntds
## knwr_lvl_c_ -0.768              
## magnitdsmll -0.255 -0.007       
## age_zscored -0.255  0.518  0.013
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                          Chisq Df Pr(>Chisq)    
## (Intercept)            20.1633  1  7.111e-06 ***
## knower_level_cp_subset  3.3854  1  0.0657766 .  
## magnitude               0.1839  1  0.6680846    
## age_zscored            11.9729  1  0.0005398 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Not registered: CP knowledge * magnitude, no age

correct_set_chosen_or_correct_count ~ knower_level_cp_subset * magnitude + (1|id) + (1|trial_ratio) Effect of KL, no interaction.

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct_set_chosen_or_correct_count ~ knower_level_cp_subset *  
##     magnitude + (1 | id) + (1 | trial_ratio)
##    Data: df.trial
## 
##      AIC      BIC   logLik deviance df.resid 
##    415.7    440.5   -201.8    403.7      462 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9427 -0.3220  0.1497  0.3829  1.8816 
## 
## Random effects:
##  Groups      Name        Variance  Std.Dev. 
##  id          (Intercept) 4.437e+00 2.1064186
##  trial_ratio (Intercept) 4.087e-08 0.0002022
## Number of obs: 468, groups:  id, 78; trial_ratio, 6
## 
## Fixed effects:
##                                             Estimate Std. Error z value
## (Intercept)                                   3.2766     0.5932   5.524
## knower_level_cp_subsetsubset                 -2.9708     0.7305  -4.067
## magnitudesmall                                0.2389     0.4895   0.488
## knower_level_cp_subsetsubset:magnitudesmall  -0.1770     0.6027  -0.294
##                                             Pr(>|z|)    
## (Intercept)                                 3.32e-08 ***
## knower_level_cp_subsetsubset                4.77e-05 ***
## magnitudesmall                                 0.626    
## knower_level_cp_subsetsubset:magnitudesmall    0.769    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) knw___ mgntds
## knwr_lvl_c_ -0.806              
## magnitdsmll -0.368  0.300       
## knwr_lvl__:  0.302 -0.386 -0.812
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                                    Chisq Df Pr(>Chisq)    
## (Intercept)                      30.5116  1  3.319e-08 ***
## knower_level_cp_subset           16.5379  1  4.769e-05 ***
## magnitude                         0.2381  1     0.6256    
## knower_level_cp_subset:magnitude  0.0863  1     0.7690    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Registered: CP knowledge * magnitude + age

correct_set_chosen_or_correct_count ~ knower_level_cp_subset * magnitude + age_zscored + (1|id) + (1|trial_ratio) Effect of age, no effect of KL or magnitude or interaction.

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct_set_chosen_or_correct_count ~ knower_level_cp_subset *  
##     magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
##    Data: df.trial
## 
##      AIC      BIC   logLik deviance df.resid 
##    404.9    433.9   -195.4    390.9      461 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3245 -0.2887  0.1606  0.3930  2.1576 
## 
## Random effects:
##  Groups      Name        Variance  Std.Dev. 
##  id          (Intercept) 3.445e+00 1.8561061
##  trial_ratio (Intercept) 6.299e-07 0.0007937
## Number of obs: 468, groups:  id, 78; trial_ratio, 6
## 
## Fixed effects:
##                                             Estimate Std. Error z value
## (Intercept)                                   2.3082     0.5542   4.165
## knower_level_cp_subsetsubset                 -1.2205     0.7633  -1.599
## magnitudesmall                                0.2343     0.4850   0.483
## age_zscored                                   1.2809     0.3703   3.460
## knower_level_cp_subsetsubset:magnitudesmall  -0.1714     0.6008  -0.285
##                                             Pr(>|z|)    
## (Intercept)                                 3.11e-05 ***
## knower_level_cp_subsetsubset                0.109813    
## magnitudesmall                              0.629029    
## age_zscored                                 0.000541 ***
## knower_level_cp_subsetsubset:magnitudesmall 0.775438    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) knw___ mgntds ag_zsc
## knwr_lvl_c_ -0.795                     
## magnitdsmll -0.398  0.292              
## age_zscored -0.243  0.483  0.011       
## knwr_lvl__:  0.322 -0.373 -0.807 -0.005
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                                    Chisq Df Pr(>Chisq)    
## (Intercept)                      17.3471  1  3.114e-05 ***
## knower_level_cp_subset            2.5569  1  0.1098129    
## magnitude                         0.2334  1  0.6290285    
## age_zscored                      11.9685  1  0.0005411 ***
## knower_level_cp_subset:magnitude  0.0814  1  0.7754381    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correct set chosen (only overt selection of set)

By trial

Higher overt correct set chosen for large sets compared to small sets. This makes sense because some participants are able to subitize small sets without pointing to the screen and count (and the prompt might not be clear enough for them to do this overtly).

## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`

By participant

Each dot is a participant. Accurracy in set chosen against age (months) looks linear.

## `summarise()` has grouped output by 'id', 'magnitude'. You can override using
## the `.groups` argument.

## `summarise()` has grouped output by 'id', 'magnitude',
## 'knower_level_cp_subset'. You can override using the `.groups` argument.
## `geom_smooth()` using formula = 'y ~ x'

Correct count

By trial

## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`

By participant

All children are better at counting small sets compared to large sets, while there is no difference in performance of selecting the correct set. So either: 1) They are doing cardinal extension, but are making errors in the counting due to the larger set, or 2) The good performance for choosing the correct set just reflects mapping of animals to a side – once the animals are gone, they just select the corresponding side without understanding the quantity relationship between the items and the animals.

## `summarise()` has grouped output by 'id', 'magnitude'. You can override using
## the `.groups` argument.

## `summarise()` has grouped output by 'id', 'magnitude',
## 'knower_level_cp_subset'. You can override using the `.groups` argument.
## `geom_smooth()` using formula = 'y ~ x'

Approximate correct count

When allowed for off by 1 error, the subset knowers are better but still worse than the CP knowers. This is not very informative anyway.

## `summarise()` has grouped output by 'id', 'knower_level_cp_subset'. You can
## override using the `.groups` argument.
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`

Comparing different measures

Error size

Absolute value of error decreases by age, and increases (slightly) as the target set correct count is bigger.

## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`
## No summary function supplied, defaulting to `mean_se()`

## `geom_smooth()` using formula = 'y ~ x'

Highest count

Highest count does not explain additional variance.

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct_set_chosen_or_correct_count ~ highest_count + magnitude +  
##     age_zscored + (1 | id) + (1 | trial_ratio)
##    Data: df.trial %>% filter(!is.na(highest_count))
## 
##      AIC      BIC   logLik deviance df.resid 
##    378.7    403.3   -183.4    366.7      438 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5513  0.0740  0.1841  0.4253  2.0294 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  id          (Intercept) 3.15456  1.7761  
##  trial_ratio (Intercept) 0.01947  0.1395  
## Number of obs: 444, groups:  id, 74; trial_ratio, 6
## 
## Fixed effects:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)    1.641653   0.431336   3.806 0.000141 ***
## highest_count  0.008775   0.016112   0.545 0.586023    
## magnitudesmall 0.087341   0.315913   0.276 0.782186    
## age_zscored    1.604187   0.354713   4.522 6.11e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) hghst_ mgntds
## highest_cnt -0.580              
## magnitdsmll -0.354  0.001       
## age_zscored  0.343 -0.290  0.014
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                 Chisq Df Pr(>Chisq)    
## (Intercept)   14.4854  1  0.0001412 ***
## highest_count  0.2966  1  0.5860235    
## magnitude      0.0764  1  0.7821864    
## age_zscored   20.4530  1  6.111e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct_set_chosen_or_correct_count ~ magnitude + age_zscored +  
##     (1 | id) + (1 | trial_ratio)
##    Data: df.trial %>% filter(!is.na(highest_count))
## 
##      AIC      BIC   logLik deviance df.resid 
##    377.0    397.5   -183.5    367.0      439 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.10693  0.07345  0.17873  0.42265  2.02737 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  id          (Intercept) 3.21857  1.7940  
##  trial_ratio (Intercept) 0.01977  0.1406  
## Number of obs: 444, groups:  id, 74; trial_ratio, 6
## 
## Fixed effects:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)      1.7855     0.3535   5.051 4.41e-07 ***
## magnitudesmall   0.0875     0.3165   0.277    0.782    
## age_zscored      1.6674     0.3422   4.873 1.10e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) mgntds
## magnitdsmll -0.433       
## age_zscored  0.225  0.015
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##               Chisq Df Pr(>Chisq)    
## (Intercept) 25.5078  1  4.406e-07 ***
## magnitude    0.0765  1     0.7822    
## age_zscored 23.7456  1  1.099e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df.trial %>% filter(!is.na(highest_count))
## Models:
## fit.base_hc_comp: correct_set_chosen_or_correct_count ~ magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
## fit.base_hc: correct_set_chosen_or_correct_count ~ highest_count + magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
##                  npar   AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)
## fit.base_hc_comp    5 377.0 397.48 -183.50    367.0                     
## fit.base_hc         6 378.7 403.28 -183.35    366.7 0.3012  1     0.5831
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: 
## correct_set_chosen_or_correct_count ~ highest_count + knower_level_cp_subset +  
##     magnitude + (1 | id) + (1 | trial_ratio)
##    Data: df.trial %>% filter(!is.na(highest_count))
## 
##      AIC      BIC   logLik deviance df.resid 
##    389.4    414.0   -188.7    377.4      438 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0679  0.1208  0.1560  0.3739  1.7952 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  id          (Intercept) 3.94844  1.9871  
##  trial_ratio (Intercept) 0.01811  0.1346  
## Number of obs: 444, groups:  id, 74; trial_ratio, 6
## 
## Fixed effects:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                   3.05874    0.71949   4.251 2.13e-05 ***
## highest_count                 0.00803    0.01904   0.422 0.673192    
## knower_level_cp_subsetsubset -2.50030    0.71917  -3.477 0.000508 ***
## magnitudesmall                0.08684    0.31379   0.277 0.781980    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) hghst_ knw___
## highest_cnt -0.632              
## knwr_lvl_c_ -0.798  0.424       
## magnitdsmll -0.205  0.001 -0.011
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                          Chisq Df Pr(>Chisq)    
## (Intercept)            18.0732  1  2.126e-05 ***
## highest_count           0.1779  1  0.6731917    
## knower_level_cp_subset 12.0873  1  0.0005077 ***
## magnitude               0.0766  1  0.7819805    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct_set_chosen_or_correct_count ~ knower_level_cp_subset +  
##     magnitude + (1 | id) + (1 | trial_ratio)
##    Data: df.trial %>% filter(!is.na(highest_count))
## 
##      AIC      BIC   logLik deviance df.resid 
##    387.6    408.0   -188.8    377.6      439 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9730  0.1392  0.1529  0.3694  1.7916 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  id          (Intercept) 3.99025  1.9976  
##  trial_ratio (Intercept) 0.01825  0.1351  
## Number of obs: 444, groups:  id, 74; trial_ratio, 6
## 
## Fixed effects:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                   3.25942    0.55999   5.820 5.87e-09 ***
## knower_level_cp_subsetsubset -2.63710    0.65419  -4.031 5.55e-05 ***
## magnitudesmall                0.08691    0.31403   0.277    0.782    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) knw___
## knwr_lvl_c_ -0.755       
## magnitdsmll -0.263 -0.012
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                          Chisq Df Pr(>Chisq)    
## (Intercept)            33.8779  1  5.868e-09 ***
## knower_level_cp_subset 16.2495  1  5.552e-05 ***
## magnitude               0.0766  1      0.782    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df.trial %>% filter(!is.na(highest_count))
## Models:
## fit.cp_hc_comp: correct_set_chosen_or_correct_count ~ knower_level_cp_subset + magnitude + (1 | id) + (1 | trial_ratio)
## fit.cp_hc: correct_set_chosen_or_correct_count ~ highest_count + knower_level_cp_subset + magnitude + (1 | id) + (1 | trial_ratio)
##                npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)
## fit.cp_hc_comp    5 387.56 408.04 -188.78   377.56                     
## fit.cp_hc         6 389.38 413.96 -188.69   377.38 0.1793  1     0.6719
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: 
## correct_set_chosen_or_correct_count ~ highest_count + knower_level_cp_subset +  
##     magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
##    Data: df.trial %>% filter(!is.na(highest_count))
## 
##      AIC      BIC   logLik deviance df.resid 
##    379.0    407.7   -182.5    365.0      437 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2627  0.0792  0.1733  0.4027  2.0125 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  id          (Intercept) 3.12300  1.767   
##  trial_ratio (Intercept) 0.02016  0.142   
## Number of obs: 444, groups:  id, 74; trial_ratio, 6
## 
## Fixed effects:
##                               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                   2.248297   0.661577   3.398 0.000678 ***
## highest_count                 0.001483   0.016959   0.087 0.930337    
## knower_level_cp_subsetsubset -0.948306   0.737789  -1.285 0.198675    
## magnitudesmall                0.087664   0.317098   0.276 0.782198    
## age_zscored                   1.331392   0.395606   3.365 0.000764 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) hghst_ knw___ mgntds
## highest_cnt -0.610                     
## knwr_lvl_c_ -0.761  0.339              
## magnitdsmll -0.229 -0.001 -0.004       
## age_zscored -0.150 -0.090  0.456  0.010
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                          Chisq Df Pr(>Chisq)    
## (Intercept)            11.5491  1  0.0006778 ***
## highest_count           0.0076  1  0.9303370    
## knower_level_cp_subset  1.6521  1  0.1986752    
## magnitude               0.0764  1  0.7821980    
## age_zscored            11.3263  1  0.0007642 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct_set_chosen_or_correct_count ~ knower_level_cp_subset +  
##     magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
##    Data: df.trial %>% filter(!is.na(highest_count))
## 
##      AIC      BIC   logLik deviance df.resid 
##    377.0    401.6   -182.5    365.0      438 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1900  0.0792  0.1722  0.4007  2.0119 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  id          (Intercept) 3.13083  1.7694  
##  trial_ratio (Intercept) 0.02022  0.1422  
## Number of obs: 444, groups:  id, 74; trial_ratio, 6
## 
## Fixed effects:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                   2.28392    0.52438   4.355 1.33e-05 ***
## knower_level_cp_subsetsubset -0.97041    0.69444  -1.397 0.162293    
## magnitudesmall                0.08768    0.31719   0.276 0.782221    
## age_zscored                   1.33463    0.39422   3.385 0.000711 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) knw___ mgntds
## knwr_lvl_c_ -0.744              
## magnitdsmll -0.289 -0.004       
## age_zscored -0.259  0.519  0.010
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                          Chisq Df Pr(>Chisq)    
## (Intercept)            18.9703  1  1.328e-05 ***
## knower_level_cp_subset  1.9527  1  0.1622929    
## magnitude               0.0764  1  0.7822206    
## age_zscored            11.4614  1  0.0007106 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df.trial %>% filter(!is.na(highest_count))
## Models:
## fit.cp_age_hc_comp: correct_set_chosen_or_correct_count ~ knower_level_cp_subset + magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
## fit.cp_age_hc: correct_set_chosen_or_correct_count ~ highest_count + knower_level_cp_subset + magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
##                    npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)
## fit.cp_age_hc_comp    6 377.02 401.59 -182.51   365.02                     
## fit.cp_age_hc         7 379.01 407.68 -182.51   365.01 0.0076  1     0.9305
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: 
## correct_set_chosen_or_correct_count ~ highest_count + knower_level_cp_subset *  
##     magnitude + (1 | id) + (1 | trial_ratio)
##    Data: df.trial %>% filter(!is.na(highest_count))
## 
##      AIC      BIC   logLik deviance df.resid 
##    391.2    419.9   -188.6    377.2      437 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1911  0.1161  0.1615  0.3875  1.8140 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  id          (Intercept) 3.95492  1.9887  
##  trial_ratio (Intercept) 0.01854  0.1362  
## Number of obs: 444, groups:  id, 74; trial_ratio, 6
## 
## Fixed effects:
##                                              Estimate Std. Error z value
## (Intercept)                                  2.989197   0.739311   4.043
## highest_count                                0.008034   0.019052   0.422
## knower_level_cp_subsetsubset                -2.387540   0.774122  -3.084
## magnitudesmall                               0.236250   0.498566   0.474
## knower_level_cp_subsetsubset:magnitudesmall -0.235870   0.610261  -0.387
##                                             Pr(>|z|)    
## (Intercept)                                 5.27e-05 ***
## highest_count                                0.67324    
## knower_level_cp_subsetsubset                 0.00204 ** 
## magnitudesmall                               0.63560    
## knower_level_cp_subsetsubset:magnitudesmall  0.69912    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) hghst_ knw___ mgntds
## highest_cnt -0.616                     
## knwr_lvl_c_ -0.806  0.395              
## magnitdsmll -0.302  0.001  0.273       
## knwr_lvl__:  0.233 -0.001 -0.368 -0.776
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                                    Chisq Df Pr(>Chisq)    
## (Intercept)                      16.3476  1  5.272e-05 ***
## highest_count                     0.1778  1   0.673244    
## knower_level_cp_subset            9.5122  1   0.002041 ** 
## magnitude                         0.2245  1   0.635600    
## knower_level_cp_subset:magnitude  0.1494  1   0.699122    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: 
## correct_set_chosen_or_correct_count ~ highest_count + knower_level_cp_subset *  
##     magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
##    Data: df.trial %>% filter(!is.na(highest_count))
## 
##      AIC      BIC   logLik deviance df.resid 
##    380.9    413.6   -182.4    364.9      436 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3895  0.0805  0.1738  0.4037  1.9693 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  id          (Intercept) 3.12850  1.7688  
##  trial_ratio (Intercept) 0.02065  0.1437  
## Number of obs: 444, groups:  id, 74; trial_ratio, 6
## 
## Fixed effects:
##                                              Estimate Std. Error z value
## (Intercept)                                  2.180124   0.683007   3.192
## highest_count                                0.001482   0.016972   0.087
## knower_level_cp_subsetsubset                -0.836031   0.793403  -1.054
## magnitudesmall                               0.233060   0.496732   0.469
## age_zscored                                  1.332197   0.395938   3.365
## knower_level_cp_subsetsubset:magnitudesmall -0.232673   0.610050  -0.381
##                                             Pr(>|z|)    
## (Intercept)                                 0.001413 ** 
## highest_count                               0.930397    
## knower_level_cp_subsetsubset                0.292007    
## magnitudesmall                              0.638936    
## age_zscored                                 0.000766 ***
## knower_level_cp_subsetsubset:magnitudesmall 0.702907    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) hghst_ knw___ mgntds ag_zsc
## highest_cnt -0.591                            
## knwr_lvl_c_ -0.777  0.315                     
## magnitdsmll -0.331 -0.001  0.272              
## age_zscored -0.148 -0.090  0.428  0.014       
## knwr_lvl__:  0.253  0.001 -0.366 -0.768 -0.011
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                                    Chisq Df Pr(>Chisq)    
## (Intercept)                      10.1885  1  0.0014132 ** 
## highest_count                     0.0076  1  0.9303973    
## knower_level_cp_subset            1.1103  1  0.2920074    
## magnitude                         0.2201  1  0.6389364    
## age_zscored                      11.3210  1  0.0007664 ***
## knower_level_cp_subset:magnitude  0.1455  1  0.7029069    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct_set_chosen_or_correct_count ~ knower_level_cp_subset *  
##     magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
##    Data: df.trial %>% filter(!is.na(highest_count))
## 
##      AIC      BIC   logLik deviance df.resid 
##    378.9    407.5   -182.4    364.9      437 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3141  0.0805  0.1725  0.4038  1.9687 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  id          (Intercept) 3.1363   1.7710  
##  trial_ratio (Intercept) 0.0207   0.1439  
## Number of obs: 444, groups:  id, 74; trial_ratio, 6
## 
## Fixed effects:
##                                             Estimate Std. Error z value
## (Intercept)                                   2.2157     0.5510   4.021
## knower_level_cp_subsetsubset                 -0.8581     0.7533  -1.139
## magnitudesmall                                0.2331     0.4968   0.469
## age_zscored                                   1.3354     0.3946   3.385
## knower_level_cp_subsetsubset:magnitudesmall  -0.2327     0.6101  -0.381
##                                             Pr(>|z|)    
## (Intercept)                                 5.79e-05 ***
## knower_level_cp_subsetsubset                0.254621    
## magnitudesmall                              0.638878    
## age_zscored                                 0.000713 ***
## knower_level_cp_subsetsubset:magnitudesmall 0.702848    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) knw___ mgntds ag_zsc
## knwr_lvl_c_ -0.772                     
## magnitdsmll -0.410  0.287              
## age_zscored -0.250  0.483  0.014       
## knwr_lvl__:  0.314 -0.385 -0.768 -0.011
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: correct_set_chosen_or_correct_count
##                                    Chisq Df Pr(>Chisq)    
## (Intercept)                      16.1713  1  5.786e-05 ***
## knower_level_cp_subset            1.2978  1  0.2546211    
## magnitude                         0.2202  1  0.6388778    
## age_zscored                      11.4561  1  0.0007126 ***
## knower_level_cp_subset:magnitude  0.1455  1  0.7028475    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df.trial %>% filter(!is.na(highest_count))
## Models:
## fit.cp_age_int_hc_comp: correct_set_chosen_or_correct_count ~ knower_level_cp_subset * magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
## fit.cp_age_int_hc: correct_set_chosen_or_correct_count ~ highest_count + knower_level_cp_subset * magnitude + age_zscored + (1 | id) + (1 | trial_ratio)
##                        npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)
## fit.cp_age_int_hc_comp    7 378.87 407.54 -182.44   364.87                     
## fit.cp_age_int_hc         8 380.87 413.63 -182.43   364.87 0.0076  1     0.9307